1/3k+1/2=1/4k

Solution for 1/3k+1/2=1/4k equation:

1/3k+1/2=1/4k

We move all terms to the left:

1/3k+1/2-(1/4k)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 4k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

1/3k-(+1/4k)+1/2=0

We get rid of parentheses

1/3k-1/4k+1/2=0

We calculate fractions


48k^2/48k^2+16k/48k^2+(-12k)/48k^2=0

Fractions to decimals

16k/48k^2+(-12k)/48k^2+1=0

We multiply all the terms by the denominator


16k+(-12k)+1*48k^2=0

Wy multiply elements

48k^2+16k+(-12k)=0

We get rid of parentheses

48k^2+16k-12k=0

We add all the numbers together, and all the variables

48k^2+4k=0

a = 48; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·48·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*48}=\frac{-8}{96}
=-1/12
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*48}=\frac{0}{96}
=0
$